[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

eXtreme Gammon question

Posted By: Timothy Chow
Date: Wednesday, 26 August 2009, at 6:52 p.m.

In Response To: eXtreme Gammon question (Keene)

The answer to the question of whether j.s.d. is equivalent to a certain confidence level is unfortunately a little complicated.

Assume that we're at double match point and that the bots play perfectly (this is the simplest case to analyze). Strictly speaking, it is still not true that a particular j.s.d. value always corresponds to the same confidence level. The confidence level answers the question, "If I declare the higher-scoring play to be the better play, what percentage of the time will I be correct?" (Note that what you're confident in is just the bare-bones statement that one play is better than the other, not the more delicate question of how much better it is.) Knowing only the j.s.d. value, you can't calculate the answer to this question. The j.s.d. is a kind of average of two separate standard deviations (one for each play), and in general you need to know both standard deviations to answer the question, not just their average. Now, in practice, the two standard deviations might be close enough to each other that you can just pretend they're equal to each other (and therefore equal to the j.s.d. value); you can then compute a confidence value based on this assumption and you probably won't be far off.

Now if you're not at double match point, then the effects of the cube and of gammons (not to mention the match score) complicate matters. The probability distributions get nastier, and the task of estimating them becomes more uncertain. Even knowing both standard deviations won't let you calculate the confidence level correctly. I don't know what backgammon programs do, but a common strategy is to ignore these difficulties and just pretend that the probability distributions are normal. This might work some of the time but you can't always trust the results.

Of course there's always the problem that bots don't play perfectly, but there's not much to be done about that.

I would assume that most users are really interested in confidence level, so I'm curious to know why the gnubg designers have gone with j.s.d. instead.

Messages In This Thread

 

Post Response
Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:
 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.